The level energies obtained by the PHF are visibly smaller than those by the PNBCS,
and the \(B(E2)\)  values obtained by the former are slightly larger than those by the latter.
This indicates that the pair correlation plays an important role in reduction of the moment of inertia but plays a limited one in reduction of the electric quadrupole transition probability;
the electric quadrupole transition strength is affected mainly by the deformation encoded in HF.
The PNBCS results may be improved if the variation of the HF single particle states is simultaneously taken into account within the NBCS variation, and result will be equivalent to that of the particle number projected Hartree-Fock-Bogoliubov [1]}, [2]}, which we leave to future work.
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